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  • Machine learning techniques for structural health monitoring

    Kay SMARSLY, Kosmas DRAGOS and Jens WIGGENBROCK

    Chair of Computing in Civil Engineering, Bauhaus University Weimar, Coudraystr. 7, 99423 Weimar (Germany) kay.smarsly@uni-weimar.de

    Key words: Structural health monitoring, machine learning, sensor fault detection, analytical

    redundancy, computer-aided structural assessment

    Abstract

    Data-driven approaches are particularly useful for computer-supported assessment of civil

    engineering structures (i) if large quantities of sensor data are available, (ii) if the physical

    characteristics of the structure are complex to model (or even unknown), or (iii) if the

    computational efforts are to be reduced. This paper, upon a classificational review of

    machine learning techniques in structural health monitoring, reports on an embedded

    machine learning approach for decentralized, autonomous sensor fault detection in wireless

    sensor networks, facilitating reliable and accurate structural health monitoring. Based on

    decentralized artificial neural networks, the embedded machine learning approach is applied

    to perform autonomous detection of sensor faults injected in the acceleration response data

    collected by a prototype structural health monitoring system. As demonstrated through

    laboratory tests, the results highlight the ability of the embedded machine learning approach

    to autonomously detect sensor faults in a decentralized manner, thus enhancing the

    reliability and accuracy of structural health monitoring systems.

    1 INTRODUCTION

    Advancements in sensor technologies have enabled economically affordable sensor

    installations for long-term monitoring of civil engineering structures. Structural health

    monitoring involves installations of hundreds to thousands of sensors to collect valuable data

    about the structure. With increasing complexity and heterogeneity of sensor data, data

    integration and data analysis have become important issues for decision making with respect

    to diagnosis of the structural condition and the prognosis of structural damage [1, 2].

    Data analysis in structural health monitoring, from a computer science perspective, aims at

    transforming sensor data into useful information and probably into knowledge about the

    structure. The information and knowledge gained from the sensor data is then used for

    structural assessment and for decision making in several respects, such as life-cycle

    management [3] or lifetime prediction [4]. Two general approaches exist for assessing the

    structural condition of civil engineering structures, physics-based approaches and data-driven

    approaches [5]. Physics-based approaches establish first-principle models, mapping the

    physical characteristics of the structure (e.g. using finite element analysis), and then compare

    the outputs of the physical models with sensor data obtained from the monitored structure in

    order to assess the structural condition [6]. Although significant efforts have been undertaken

    to render physics-based models more efficient in terms of computational performance, for

    example for embedment into resource-constraint wireless sensor nodes [7, 8], physics-based

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    approaches are generally more computationally intensive than data-driven approaches.

    Data-driven approaches also establish models for comparison with sensor data, but data-

    driven models exploit information from previously collected sensor data, referred to as

    training data [9]. While physics-based approaches are valid in a large operating range

    without the need for extensive quantities of sensor data, data-driven approaches allow

    learning patterns in the sensor data without any knowledge on the physical characteristics of

    the structure [10]. Data-driven approaches are particularly useful, if (i) large quantities of

    sensor data are available, (ii) the physical characteristics of the structure are complex to

    model (or even unknown), or (iii) the computational efforts are to be reduced.

    A variety of data-driven approaches, particularly machine learning techniques, has been

    proposed in structural health monitoring (SHM) for assessing civil engineering structures.

    Machine learning in the context of SHM can be described as the task of generating

    knowledge from past experiences (or, more precisely, from collected sensor data), focusing

    on the prediction of new sensor data. While in artificial intelligence research machine

    learning techniques have been studied since many decades (e.g. for robot control, human-

    computer interaction, or speech recognition), its importance in SHM applications

    substantially continues to grow since about 20 years [11, 12]. For example, Worden and

    Manson [13] have illuminated the utility of machine learning to damage identification,

    concluding that neural networks are still popular, and systems like support vector machines

    are beginning to appear more regularly. Figueiredo et al. [14] have investigated auto-

    associative neural networks, factor analysis, Mahalanobis distance, and singular value

    decomposition to study operational and environmental variability and its influence on

    damage detection of civil engineering structures. Dervilis [15], centered on SHM of wind

    turbine blades, also explores auto-associative neural networks and formulates pattern

    recognition algorithms. In addition, robust multivariate statistical methods are introduced to

    account for the influence of operational and environmental variation on damage-sensitive

    features; the algorithms described are the Minimum Covariance Determinant Estimator and

    the Minimum Volume Enclosing Ellipsoid. Park et al. [16], also focusing on wind energy

    research, couple Gaussian Discriminative Analysis and Gaussian Mixture Models to analyze

    and to predict wind turbine loads in various atmospheric conditions. Nick et al. [17],

    reporting significant trade-offs between accuracy and runtime of the machine learning

    techniques proposed, have used unsupervised learning for identifying the existence and

    location of damage (k-means and self-organizing maps) and supervised learning for

    identifying the type and severity of damage (support vector machines, naive Bayes

    classifiers, and feed-forward neural networks).

    This paper presents an embedded machine learning approach for decentralized,

    autonomous fault detection in wireless SHM systems. Sensor faults and miscalibrations

    substantially affect sensor data and may compromise the reliability and accuracy of SHM

    systems. Specifically in data-driven approaches, the integrity of the sensor data needs to be

    preserved to enhance the reliability and accuracy of SHM system outputs as well as the

    robustness of algorithms implemented for structural health monitoring. In the study reported

    in this paper, the efficient detection of sensor faults and miscalibrations is based on the

    correlations among the response data of different sensor nodes, referred to as analytical

    redundancy, which is implemented through an embedded machine learning approach based

    on artificial neural networks. This paper is organized as follows: First, an overview of

    machine learning techniques commonly used in structural health monitoring is provided.

    Then, the embedded machine learning approach for decentralized, autonomous sensor fault

    detection, based on artificial neural networks, is implemented into a wireless SHM system.

  • 3

    Serving as a testbed for the proposed approach, a laboratory test structure is used in this paper

    for validation, followed by a concise summary of the study presented herein.

    2 AN EMBEDDED MACHINE LEARNING APPROACH FOR DECENTRALIZED,

    AUTONOMOUS SENSOR FAULT DETECTION

    In computer science and in computational engineering, the process of detecting patterns

    and structures within data sets is commonly known as data mining. The detection of patterns

    enables future predictions and decision making, while representing the patterns in terms of

    structures facilitates the extraction of conclusions on the patterns. In data mining, the

    techniques employed to detect patterns within data sets fall into the category of machine

    learning.

    As mentioned previously, due to the computational burden of physics-based approaches in

    structural health monitoring, data-driven approaches, such as machine learning, have been

    gaining increasing attention. In SHM, machine learning is understood as the task of

    generating knowledge about the structural behavior from previously collected sensor data.

    While structural responses are theoretically well explained and documented, the detection of

    such responses in full-scale structures is non-trivial due to the complex nature of actions and

    the actually unknown properties of the structure. Furthermore, SHM outputs may be affected

    by sensor faults and miscalibrations, which may be hardly visible in the collected data. In this

    context, machine learning is applied to detect such hidden, non-evident, or inadequately

    described phenomena. In this section, the machine learning techniques typically applied in

    SHM are briefly discussed. Then, an embedded machine learning approach for decentralized,

    autonomous detection of sensor faults and miscalibrations is presented.

    2.1 Classification of machine learning techniques for structural health monitoring

    Machine learning techniques can be classified into three broad categories according to the

    nature of learning: 1) supervised learning, 2) unsupervised learning, and 3) semi-supervised

    learning [18]. Supervised learning provides a learning scheme with labeled data, i.e.

    examples that include specified outputs (pairs of input data and output data). Using labeled

    data, rules are developed in an attempt to classify new data sets. Unsupervised learning

    encompasses the detection of patterns within the data sets consisting of unlabeled data, i.e.

    data sets with unspecified outputs, which fit to a general rule and can, therefore, be grouped

    together. From an SHM viewpoint, unsupervised learning can be used, e.g., for detecting the

    existence of damage through clustering of structural response data, while supervised learning

    can advantageously be employed to detect the type and severity of damage [19]. Semi-

    supervised learning, representing a combination of the two aforementioned learning schemes,

    typically aims at obtaining a classification of data using both labeled and unlabeled data.

    Semi-supervised learning schemes have been applied combined with other monitoring

    techniques to extract information on modal characteristics of bridges [20].

    Since most SHM problems require inferring a function from labeled training data (e.g. to

    assess the data or to predict new data), supervised learning is an appropriate means to solve

    these problems. In supervised learning, the algorithms, according to [21], can be categorized

    as logic-based algorithms (e.g., decision trees and rule-based classifiers), perceptron-based

    algorithms or neural networks (e.g., single-layered perceptron, multi-layered perceptron and

    radial basis function networks), statistical learning (e.g., naive Bayes classifiers and Bayesian

    networks), instance-based learning (e.g., k-nearest neighbor algorithm), and support vector

    machines.

  • 4

    2.2 Prototype implementation of the machine learning approach

    In this study, decentralized autonomous sensor fault detection is based on the principle of

    analytical redundancy [22]: Instead of physically installing multiple sensors for measuring

    one single parameter, analytical redundancy takes advantage of the redundant information

    inherent in the SHM system and utilizes the coherences and relationships between the sensors

    installed in the structure. It has been proven that the peak amplitudes of the frequency

    spectrum, obtained by the Fourier transformation of acceleration response data,

    corresponding to resonant response (i.e. modal peak amplitudes) from different sensors of the

    same structure are correlated [23]. This correlation can be exploited to predict the modal peak

    amplitudes of selected sensors, using the modal peak amplitudes of correlated sensors as

    input data. Deviations between expected amplitudes and actual amplitudes (i.e. from the

    measured data) are indicative of sensor faults and miscalibrations. Importantly, no a priori

    knowledge about the structure or about the sensor instrumentation is required because, as a

    purely data-driven approach, previously collected sensor data is taken as the sole basis for

    fault detection.

    A wireless SHM system is designed that comprises wireless sensor nodes, each of which

    including an integrated 3-axis accelerometer, a base station, and a host computer. The

    monitoring tasks executed by the SHM system are illustrated in Figure 1. During operation,

    acceleration response data is sampled by each sensor node and locally transformed into the

    frequency domain via an embedded Cooley-Tukey FFT algorithm. A peak detection

    algorithm selects the highest peak of the frequency spectrum corresponding to the

    fundamental eigenfrequency (modal peak amplitude), and the modal amplitudes are

    communicated among the sensor nodes. Each sensor node predicts the modal amplitude of its

    own acceleration response data (expected amplitude) using the modal peak amplitudes of

    correlated sensor nodes and decides upon the existence of sensor faults based on deviations

    between the expected and the actual modal peak amplitude. The outcomes of the fault

    detection procedure of the sensor nodes are transmitted to the host computer via the base

    station for storage and decision making.

    Figure 1. Decentralized, autonomous fault detection procedure executed by the wireless SHM system

  • 5

    The decentralized autonomous fault detection procedure proposed in this study relies on

    the relationships among the modal peak amplitudes from different sensors. To map these

    relationships an embedded machine learning approach with a supervised learning scheme is

    introduced. To this end, artificial neural networks (ANNs) are designed and distributedly

    embedded into each sensor node. As shown in Figure 2, the ANNs consist of three layers of

    neurons: 1) an input layer of k neurons, 2) a hidden layer of m neurons to account for the non-

    linear relationship among the modal peak amplitudes of different sensors [24], and 3) an

    output layer of one neuron, which represents the predicted modal peak amplitude of the

    sensor under consideration. The data is propagated through the ANN via the synapses (i.e.

    connections between neurons), based on the weight of each connection. During the ANN

    training, the weights of the synapses are adjusted until a selected set of input data results in

    the desired output data. The ANN properties (i.e. ANN topology and neuron behavior) are

    determined based on computational steering and trial-and-error tests. For further details, the

    interested reader is referred to [9, 22, 24, 25].

    Figure 2. Schematic of the artificial neural network embedded into the wireless sensor nodes

    3 VALIDATION OF THE MACHINE LEARNING APPROACH

    Validation tests to showcase the ability of the embedded machine learning approach are

    performed on a laboratory test structure. In the first part of this section, the laboratory test

    setup is described. In the remainder of this section, the training of the ANN and the

    determination of the ANN properties are presented. Finally, the application of the embedded

    machine learning approach is illuminated.

    3.1 Laboratory test setup

    To validate the embedded machine learning approach, the wireless sensor nodes are

    installed on the test structure, as shown in Figure 3. The test structure is a 4-story frame

    structure consisting of steel plates of 250 mm x 500 mm x 0.75 mm. The plates are mounted

    on threaded rods with a vertical clearance of 23 cm. At the bottom of the structure, the rods

    are fixed into a solid block of 400 mm x 600 mm x 300 mm. A total of four wireless sensor

    nodes, labeled A, B, C and D, are placed on the structure at the center of each story.

    In addition to the wireless sensor nodes, a base station, connected to a local computer, is

    placed next to the test structure.

  • 6

    Figure 3. Schematic of the laboratory test structure

    3.2 Training and determination of the artificial neural network properties

    Preliminary tests are conducted to determine the ANN properties [24]. Several

    combinations of topologies and neuron behaviors are tested. The determination of the

    properties is based on the performance of the ANN in terms of time required for training and

    on the output accuracy. The output accuracy (or the predictive power) is expressed through

    the root mean squared error between the expected and the actual amplitudes, as shown in Eq.

    1. For training, 100 sets of 4 modal peak amplitudes (from all sensor nodes) are created.

    Following the standard practice in ANN training, the data set is divided to 80% training sets

    to establish the relationship between inputs and outputs, 10% validation sets to decide when

    to stop training, and 10% test sets to check the predictive power of the trained ANN.

    Ni

    iactual,iexpected,RMS FFN 1

    2

    1

    2

    1

    1 (1)

    In Eq. 1, RMS is the root mean squared error, N is the number of testing sets, Fexpected is the expected modal peak amplitude, Factual is the actual amplitude, and 1 is the fundamental eigenfrequency. The sets of modal peak amplitudes are split into three inputs and one output;

    the modal peak amplitudes of sensor nodes A, C, and D are used as input to predict the modal

    peak amplitude of sensor node B. Therefore, each of the tested ANNs has three neurons in

    the input layer and one neuron in the output layer. Between the input layer and the output

    layer, several hidden layers with varying number of neurons per hidden layer are tested. In

    terms of neuron connections, both interlayer connections (between adjacent neurons) and

    supralayer connections (i.e. between distant neurons) are tested. Finally, for neuron behavior,

    both backpropagation and resilient backpropagation algorithms are applied. The results of the

    preliminary tests are presented in Table 1.

  • 7

    Neuron behavior Topology Neurons per

    sensor node

    Computing

    time (s)

    RMS (-)

    Interlayer,

    backpropagation

    3-1 4 6.6 0.149

    3-2-1 6 13.0 0.102

    3-3-1 7 17.2 0.144

    3-5-1 9 25.0 0.081

    3-7-1 11 32.2 0.063

    3-2-2-1 8 21.0 0.092

    3-5-5-1 14 46.6 0.137

    Interlayer and

    supralayer,

    backpropagation

    3-3-1 7 15.2 0.147

    3-5-1 9 22.6 0.132

    3-2-2-1 8 19.4 0.137

    Interlayer, resilient

    backpropagation

    3-3-1 7 113.0 0.153

    3-5-1 9 172.4 0.143

    3-2-2-1 8 120.6 0.208

    Table 1. Results of preliminary tests to determine the ANN properties (source: [24])

    The results of the preliminary tests show that all combinations of ANN properties

    demonstrate satisfactory output accuracy. However, in terms of performance the time

    required for training varies significantly. As a trade-off between the time and the output

    accuracy an ANN with 3-2-1 topology, interlayer connections, and backpropagation neuron

    behavior is selected. In the next subsection, the application of the selected ANN to detect

    sensor faults injected into the acceleration response data is presented.

    3.3 Application of the machine learning approach for autonomous fault detection

    Two of the most common fault types, bias and precision degradation, are simulated and

    injected into the acceleration response data. A bias (Figure 4a) is a deviation between the

    actual response and the expected response by a constant value; precision degradation (Figure

    4b) is a contamination of the response data with excessive-variance white noise. Both faults

    have a noticeable impact on the modal peak amplitudes of the acceleration response data.

    Figure 4. Manifestations of bias (a) and precision degradation faults (b)

    Figure 5. Impact of the simulated and injected sensor faults on the modal peak amplitudes

  • 8

    Bias is injected by rotating one sensor node by 45o, while precision degradation is injected

    by contaminating the acceleration response data of the sensor nodes with a random Gaussian

    time series. Similar to the preliminary tests, the modal peak amplitudes from sensor nodes A,

    C, and D, (as depicted in Figure 3) are used to predict the modal peak amplitude of sensor

    node B. A threshold for the RMS at = 0.15 is established from trial-and-error tests. The results of the ANN application are summarized in Table 2.

    Root mean square error No fault

    Simulated fault

    Bias Precision

    degradation

    RMS 0.102 0.603 0.807

    Table 2. Fault detection of simulated sensor faults, indicated by root mean square error.

    As shown in Table 2, the root mean squared error for both simulated sensor faults

    significantly exceeds the predefined threshold. It can be concluded that fault detection using

    the proposed embedded machine learning approach is a promising tool to enhance the

    reliability and accuracy of monitoring.

    4 SUMMARY AND CONCLUSIONS

    A broad wealth of data-driven approaches, particularly machine learning approaches, has

    been proposed in structural health monitoring for assessing the condition of civil engineering

    structures. In machine learning approaches for structural health monitoring, the learning

    scheme can be categorized into supervised, unsupervised, and semi-supervised learning.

    Based on supervised learning, an embedded machine learning approach for decentralized

    autonomous fault detection has been presented in this paper. The proposed approach makes

    use of the analytical redundancy, i.e. the redundant information obtained by the sensors.

    More specifically, the inherent correlations among the amplitudes at peaks of the frequency

    spectra of acceleration response data obtained from different sensors are utilized. The modal

    peak amplitude of each sensor is predicted using the modal peak amplitudes of correlated

    sensors as input data. Deviations between the expected amplitude (i.e. the amplitude obtained

    from the prediction) and the actual amplitude are indicative of sensor faults. To map the

    relationship among the modal peak amplitudes of correlated sensor nodes, artificial neural

    networks have been distributedly embedded into the wireless sensor nodes.

    Validation tests have been conducted on a 4-story laboratory test structure. A total of four

    wireless sensor nodes have been used, each of which placed at the center of one story.

    Preliminary tests have been performed to determine the properties of the ANN, based on time

    and output accuracy criteria, in which the modal peak amplitudes of the sensor nodes of three

    stories have been used to predict the modal peak amplitude of the sensor node of the

    remaining story. Then, two common sensor faults have been injected into the acceleration

    response data of one sensor node. Finally, the ANN has been applied, and, using the modal

    peak amplitudes of the other three sensor nodes the faults have been successfully detected. In

    conclusion, the results of the validation tests showcase the ability of the proposed machine

    learning approach to detect sensor faults. Future work could include establishing a solid

    threshold to distinguish non-faulty from faulty operation as well as implementing the

    automated adaptation of the fault detection procedure to account for structural changes.

  • 9

    5 ACKNOWLEDGMENTS

    Financial support of the German Research Foundation (DFG) through the Research

    Training Group 1462 is gratefully acknowledged. Any opinions, findings, conclusions or

    recommendations expressed in this paper are solely those of the authors and do not

    necessarily reflect the views of DFG or any other organizations and collaborators.

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